The approximation of flows |
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Authors: | Derek W Robinson |
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Institution: | 1. Département de Physique, Université d''Aix-Marseille Marseille, France;2. Centre de Physique Théorique, CNRS, Marseille, France |
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Abstract: | Let U, V be two strongly continuous one-parameter groups of bounded operators on a Banach space with corresponding infinitesimal generators S, T. We prove the following: ∥Ut, ? Vt ∥ = O(t), t → 0, if and only if U = V; ∥Ut ? Vt∥ = O(tα), t → 0; with 0 ? α ? 1, if and only if , where Ω, P, are bounded operators on such that if and only if has a bounded extension to 1. Further results of this nature are inferred for semigroups, reflexive spaces, Hilbert spaces, and von Neumann algebras. |
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